standard form problem solving worksheet

Standard Form: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

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Standard Form Worksheet and Answer Key

Students will practice working with the Standard Form Equation of a Line including finding the X and Y-intercept s, Graphing Standard Form Equations and converting Slope Intercept to Standard Form .

Example Questions

Find the x - and y - intercepts of the Standard Form Linear Equations below.

Write each equation in Standard Form using integer coefficients for A, B and C.

Graph each line using intercepts.

Other Details

This is a 4 part worksheet:

• Part I Model Problems
• Part II Practice
• Part III Challenge Problems
• Part IV Answer Key
• Slope Intercept Form to Standard Form
• Slope Intercept to Standard Form
• Standard to Slope Intercept
• Equation of Line Formulas
• Linear Equation Links, Lessons and Tutorials
• Standard Form to Point Slope Form
• Point Slope to Standard Form

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Standard Form Problem Solving worksheet

Total reviews: (0), standard form problem solving worksheet description.

If you are needing some extra worded questions on standard form, then this worksheet has three questions to test your learners comprehension and problem-solving skills.

Section A has a problem that will involve find the difference between two planets.

Section B adds the repeated percentage change.

Section C looks at a problem about cell size and will involve both multiplication and division.

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Standard Form Worksheets

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• Standard Form

Our collection of free printable standard form worksheets helps young learners to write numbers in the standard form as well as they learn to identify the place values of their digits. The exercises here put forth whole numbers ranging from 2 digits to multiple digits and decimals in the expanded form and require students to convert them into the standard form.

This set of standard form worksheets is perfect for children in grade 1 through grade 5.

List of Standard Form Worksheets

Writing 2-Digit Numbers in the Standard Form

Writing 3-Digit Numbers in the Standard Form

Writing 4-Digit Numbers in the Standard Form

Writing 5-Digit Numbers in the Standard Form

Writing 6-Digit Numbers in the Standard Form

Writing Multi-Digit Numbers in the Standard Form

Writing Decimals in the Standard Form

Greet a heartfelt hello to your standard form practice with this simple practice batch! Write the digits in the appropriate places and express the expression in the standard form.

Swing into some spirited conversion action with this set of pdf worksheets for 1st grade, 2nd grade, and 3rd grade! Express the 3-term expansion as a 3-digit number in the standard form.

Let not having to write 4-digit numbers in standard forms put you in a spot of bother! Try solving these printable worksheets for grade 1, grade 2, and grade 3, and delve deeper into the topic of place value!

Study the addends in these standard form pdfs, and figure out the digits that hold the ten thousands, thousands, hundreds, tens, and ones places of a 5-digit number.

Learn to express 6-digit numerals in the standard notation with this set of pdfs designed for grade 4 and grade 5 kids! Decode the digits from the expanded form and write down the whole number with ones to hundred thousands places.

Students in 4th grade or 5th grade are now totally at home in their standard form tasks. Determine which of the 7-digit, 8-digit, and 9-digit numbers stands for the 20+ expressions here.

Unit fractions with multiples of ten in the denominator denote the place values of the decimal part of a number. Use this simple fact and condense an expansion to the decimal notation with this collection of decimals in standard form worksheets!

Related Printable Worksheets

▶ Expanded Form

▶ Abacus

▶ Base Ten Blocks

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Standard Form Worksheet

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Help your students prepare for their Maths GCSE with this free comparing Standard Form worksheet of 44 questions and answers

• Section 1 of the Standard Form worksheet contains 12 skills-based Standard Form questions, in 3 groups to support differentiation
• Section 2 contains 4 applied Standard Form questions with a mix of worded problems and deeper problem solving questions
• Section 3 contains 4 foundation and higher level GCSE exam style Standard Form questions 
• Answers and a mark scheme for all Standard Form questions
• Follows variation theory with plenty of opportunities for students to work independently at their own level
• All questions created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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Standard form at a glance

Standard form, or standard index form, is a simple way of writing very large numbers or very small numbers. To write a number in standard form, we write the number as a decimal between 1 and 10, multiplied by a power of 10.  We call numbers that are not written in standard form ordinary numbers.

When converting numbers to standard form, we write any significant figures as a decimal between 1 and 10. We then need to maintain the place value of the number by multiplying the decimal by a power of 10. For example let’s look at the number 43000. The significant figures here are 4 and 3 so the decimal is 4.3. To maintain the place value of the number, we need to multiply 4.3 by 10000 or 10 4 . Therefore 43000 can be written as 4.3×10 4 . For very small numbers, the power of 10 will be negative. 

We can convert standard form numbers back to ordinary numbers by multiplying the decimal by the power of 10. We can multiply and divide numbers written in standard form directly but to add or subtract numbers written in standard form it is best to convert them back to ordinary numbers. 

Looking forward, students can then progress to additional number worksheets , for example a fractions worksheet or a rounding worksheet .

  For more teaching and learning support on Number our GCSE maths lessons provide step by step support for all GCSE maths concepts.

Related worksheets

GCSE Exam Questions – Adding and Subtracting Surds

GCSE Exam Questions – Multiplying and Dividing Surds

GCSE Exam Questions – Rationalise the Denominator

GCSE Exam Questions – Simplifying Surds

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Standard and Expanded Form Worksheets

This ensemble of printable worksheets is exclusively designed for students of grade 1 through grade 5, to help them write numbers in standard form to expanded form and vice versa. The worksheets are split into place values of units, thousands, millions and billions to enable convenient downloads. A number of free worksheets are at your disposal.

Standard and Expanded Form: Units Place Value

Task 1st grade and 2nd grade kids to convert a mix of 2-digit and 3-digit numbers from standard form to expanded form and vice versa.

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Standard and Expanded Form: Thousands Place Value

Transform numbers that contain place values of thousands to expanded form and vice versa. Provide ample practice for young learners with 15 pdf worksheets in this section.

Standard and Expanded Form: Millions Place Value

This practice set requires 3rd grade and 4th grade children to rewrite the standard numeric notations that comprise place values in millions, into expanded form and contrariwise.

Standard and Expanded Form: Billions Place Value

Convert the given multi-digit numbers from standard form into expanded form and vice versa.

Standard and Expanded Word Form Worksheets

This wide collection of printable worksheets requires students to convert numbers into expanded word form and vice versa.

(70 Worksheets)

Standard and Expanded Product Form Worksheets

Transform the numbers provided in these worksheets to expanded product form and contrariwise. In product form, the digits will be accompanied by place value multipliers expressed in multiples of 10s.

(60 Worksheets)

Standard and Expanded Exponent Form Worksheets

Teach students of 5th grade and above the basic exponent rules to help them solve this compilation of pdf worksheets that focus on powers of 10. Rewrite numbers in standard form and exponential form.

Standard and Expanded Form - Decimals Worksheets

Grasp different ways of writing decimals in expanded notation with this ensemble of worksheets. Learners will need to transform decimals in place value form, exponential form and in the form of unit fractions.

(90 Worksheets)

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Rewriting Linear Equations in Standard Form (A)

Welcome to The Rewriting Linear Equations in Standard Form (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2015-04-22 and has been viewed 632 times this week and 508 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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Standard Form

Standard form in maths is the method of representing a particular element in the most common manner. From large numbers to small numbers to equations to lines, every element in maths is denoted in a standard form. Let us explore this interesting concept of standard form in various elements of maths such as fractions, equations, algebra, slope along with learning the standard from formula. Solving examples and understanding the basic thumb rule will help in understanding the concept better.

What is Standard Form?

A standard form is a form of writing a given mathematical concept like an equation, number, or an expression in a form that follows certain rules. Representing very large or very small numbers concisely, the standard form is used. For example, 4.5 billion years is written as 4,500,000,000 years. As you can see here, writing a large number like 4.5 billion in its number form is not just ambiguous but also time-consuming and there are chances that we may write a few 0’s less or more while writing in the number form. In this case, writing the number in standard form is very helpful. For example, the standard form of 4,500,000,000 = 4.5 × 10 9 . Not only numbers but the fractions, equations, expressions, polynomials, etc also can be written in the standard form.

Let us study the standard form of each of these in detail.

Standard Form of Number

The standard form of numbers (which is also known as " scientific notation " of numbers)  has different meanings depending on which country you are in. In the United Kingdom and countries using UK conventions, the standard form is another name for scientific notation. Scientific notation is the process of writing a very large or very small number using numbers between 1 to 10 multiplied by the power of 10. For example, 3890 is written as 3.89 × 10 3 . These are numbers that are greater than 1 use positive powers of 10. Numbers less than 1 use the negative power of 10. For example, 0.0451 is written as 4.51 × 10 -2 .

In the United States and countries using US conventions, the standard form is the usual way of writing numbers in decimal notation . Using the same example,

Standard form = 3890, Expanded form = 3000 + 800 + 90, and Written form = Three thousand eight hundred and ninety.

Standard Form of Fraction

In the case of fractions, we need to ensure that in the standard form of fractions, the numerator and denominator must be co-prime numbers . That means they have no common factor other than 1, hence the standard form is also called the simplest form of a fraction . For example, 14/22 and 13/6. The simplest form of 14/22 = 7/22 and 13/6 is already in its simplest form as 13 and 6 are co-prime.

Standard Form of Equations

The standard form of an equation is where zero goes on the right and everything else goes on the left. i.e., it is of the form

• Expression = 0.

This helps in solving the equation in a simple manner. Equations used for polynomials, linear and quadratic have a standard form, let us look at what they are.

Standard Form of Polynomial

The standard form polynomial is written with the exponents in decreasing order to make calculations easier. A polynomial is said to be in its standard form, if it is expressed in such a way that the term with the highest degree is placed first, followed by the term which has the next highest degree, and so on. There are two very simple rules of writing a polynomial in a standard form, they are:

• Write the terms in the descending order of their powers (also called exponents).
• Ensure the polynomial contains no like terms.

Hence, the standard form is a n x n  + a n-1 x n-1  + a n-2 x n-2  + ... + a 1 x 1  + a 0 . For example, the standard form of equation y 2 + 7y 6 - 8y - y 9 is written as -y 9 + 7y 6 + y 2 - 8y.

Note: The thumb rule for writing a polynomial in its standard form is D-U. D stands for Descending and U stands for unlike terms.

Standard Form of a Linear Equation

The standard form of linear equations also known as the general form is a method of writing linear equations. A linear equation can be written in different forms like the standard form, the slope-intercept form, and the point-slope form . The standard form of a linear equation is expressed in two ways, with one variable and with two variables . The standard form of linear equation with one variable is expressed as ax + b = 0 where a and b are constants and the letters x is the variable. The standard form of a linear equation with two variables is expressed as ax + by = c. where a, b, and c are real numbers and the letters x and y are the variables. Look at the image below.

Let’s see how to convert the two lines into the standard form of a linear equation ax + by = c.

Line 1: x + y = 7 i.e. 1x +1y = 7. Here, a = 1, b =1 , c = 7

Line 2: y = 3x i.e. 3x -1y = 0. Here, a = 3, b = -1 , c = 0

Therefore, what we see here is the standard form of equation which is linear i.e. ax + by = c.

Standard Form of Slope of a Line

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. Representing a line geometrically, we use the standard form of a linear equation (mentioned above). To determine the slope of a line that is expressed graphically, the equation must be converted to a slope-intercept form . To do this, we must solve the equation for y, and the standard form of a slope is expressed as y = mx + c, where m is the slope of the line. This formula is used when the line is straight.

When there are two points in a plane , the slope can be defined as the ratio of change in the value of y to the change in the value of x. The standard form of slope of a line is expressed as m = (y 2 – y 1 )/(x 2 – x 1 ). The image below represents both the coordinates on a graph.

Standard Form of Quadratic Equations

The standard form of quadratic equation in a variable x is of the form ax 2 + bx + c = 0, where a ≠ 0, and a, b, and c are real numbers . Here, b and c can be either zeros or non-zero numbers and

• 'a' is the coefficient of x 2
• 'b' is the coefficient of x
• 'c' is the constant

Apart from the standard form of a quadratic equation, a quadratic equation can be written in several other forms.

• Vertex Form: a (x - h) 2 + k = 0
• Intercept Form: a (x - p)(x - q) = 0

A parabola is a graph of a quadratic function that refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed-line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola . The following graphs are two typical parabolas; their x and y-intercepts are marked by green dots, and the vertex of each parabola is marked by a blue dot.

The graph will have one of the two shapes as shown above.

• When a > 0, it represents the first parabola (figure 1) which opens upward (U-shaped).
• When a < 0, we obtain a parabola that opens downward (inverted U-shaped) as shown in figure 2.

When we put y = 0 in the above equation, we get the x-intercept which is also called the roots of the equation . Finding the roots provides us with the turning point of the parabola and the vertical line which is drawn from the turning point is called the axis of symmetry . Look at the image below for reference.

Standard Form Formula

The standard form formula represents the standard form of an equation which is the commonly accepted form of an equation. The formula to represent the standard form formula is based on the degree of the equations.

The standard form of a linear equation is the basic form of an equation. The standard form of a linear equation with two variables and more than two variables is presented below. Here x, y, or x 1 , x 2 , x 3 ,.... represent the variables and a, b, a 1 , a 2 , a 3 , ........ a n are referred to as the coefficients. The numerics placed to the right of the equals to sign are called constants.

ax + by = c

a 1 x 1 +a 2 x 2 + a 3 x 3 + ........ + a n x n = D

The standard form of a quadratic equation is a second-degree equation and has a variable, coefficients, and constant term. Here it is a single variable x of degree 2. The standard form of a quadratic equation is ax 2 + bx + c = 0, where a ≠ 0.

Further, we have standard form formulas for equations of higher degrees. Also in coordinate geometry , we have a standard form for different geometric representations such as a straight line, circle , ellipse , hyperbola , and parabola.

• Straight-line: ax + by = c, where a is a positive integer , and b, and c are integers.
• Circle: (x - h) 2 + (y - k) 2 = (r) 2 , where ( h, k) is the center and r is the radius .
• Ellipse: x 2 /a 2  + y 2 /b 2  = 1
• Hyperbola: (x-x 0 ) 2 /a 2  - (y-y 0 ) 2 /b 2  = 1, where x 0 , x 0 are the center points, a = semi-major axis and b = semi-minor axis.
• Parabola: (x - h) 2 = 4p(y - k)

☛Related Topics

Listed below are a few topics that are related to a standard form.

• Standard Form Calculator
• Standard Form to Vertex Form
• Polynomial in One Variable in Standard Form

Standard Form Examples

Example 1: Liza is trying to find out which of the following equations represent the given graph. As there are no values of the coordinates given, she is not able to decide. How can we use the standard form concept to solve her problem?

1. x 4 + 7x 2 - 5x = 4

2. 4x + 5y = 0

3. y 2 + 7y 6 - 9y = y 3

4. 3z 4 + 7z 5 = -12z

The graph given here represents a line . Now, a line represents a linear equation in two variables which has a degree of 1. Out of the four equations given above, only option (b) is linear.

Answer:  Therefore, the graph represents the equation, 4x + 5y = 0.

Example 2: Anna showed her class notes on polynomials to her teacher. The teacher returned her notes with a remark "Write the polynomial x 2 -10x + 16- x 2 + x 5 - 3x 4 + 3x 2 in standard form." What is the correct format Anna should have used?

To write a polynomial in standard form, two rules must be taken care of.

1. Write the terms in descending order of their powers.

2. All terms must be unlike.

Let us first arrange in descending order .

x 2 - 10x + 16- x 2 + x 5 - 3x 4 + 3x 2 = x 5 - 3x 4 + x 2 - x 2 + 3x 2 - 10x +16

After adding like terms , we get

x 5 - 3x 4 +3x 2 - 10x + 16.

Answer:  Therefore, the standard form is x 5 - 3x 4 +3x 2 - 10x + 16.

Example 3: Convert the following quadratic equation into standard form: (1/x) + x = 1.

(1/x) + x = 1

Multiplying with x on both sides,

1 + x 2 = x

Shifting R.H.S. terms to L.H.S.,

x 2 - x + 1 = 0

Answer:  Therefore, Standard form of the given quadratic equation is x 2 - x + 1 = 0.

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Practice Questions on Standard Form

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FAQs on Standard Form

What is the definition of standard form in math.

Standard form in math is the method of representing a particular element (numbers, fractions, equations, etc) in the most common way. Very large numbers or very small numbers are expressed in the standard form. Mathematical elements such as equations are expressed in a standard form to better solve the problem. In other words, a standard form is a form of writing a given mathematical concept like an equation, number, or expression in a form that follows certain rules.

How Do We Write Standard Form in Maths?

The process of writing a given mathematical concept like an equation, number, or expression in certain rules is called the standard form. Depending upon which mathematical concept we are dealing with, the standard form formula will vary.

How Do You Write Standard Form of Number?

Standard form in math of numbers is written differently depending on the country. In the UK, numbers that are greater than 1 use positive powers of 10, and numbers less than 1 use the negative power of 10. For example, 3670000 is written as 3.67 × 10 6 and 0.0763 is written as 7.63 × 10 -2 . This is commonly known as scientific notation of numbers.

What is Standard Form Formula?

The standard form formula refers to the formula presenting the general representation for different types of notation. For example, the standard form of

• a linear equation is ax + by = c.
• a quadratic equation is ax 2  + bx + c = 0
• a cubic equation is ax 3  + bx 2  + cx + d = 0

What is the Standard Form Formula for Parabola?

The standard form formula of the equation of the parabola is this: (y - k) 2 = 4p(x - h), where p≠ 0 only in case a parabola has a horizontal axis.

• The vertex of this parabola is at (h, k).
• The focus is at (h + p, k).

What is the Standard Form for Slope Formula?

The standard form of the  slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line whereas the standard form of a linear equation is Ax + By = C and the slope in this form is -A/B.

How to Use Standard Form Formula?

We can use the standard form formula depending on the equation, if it's linear, quadratic, etc. Just rewrite the given formulas in the standard form.

• Standard form of linear equation : ax + by = c
• Standard form of a quadratic equation is a second degree equation: ax 2 + bx + c = 0

What is the Standard Form of Equation?

In the standard form of an equation, 0 is usually present on the right side, whereas the rest of the expressions are on the left. Also, the terms are arranged in the descending order of their exponents. To convert an equation into stadard form, just apply arithmetic operations on both sides to turn the right side to be 0.

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Problems using Standard Form - With Answers

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

2 January 2023

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