Numbers Worksheets

Practice and master numbers with our helpful walkthroughs and downloadable practice worksheets from our team of elite math educators.

Standard Form of a Number-also known as Standard Index Form

By Gina Vaughan Faragher

Standard form of a number is a method for communicating very small or very large numbers quickly and easily. Also called scientific notation or standard index form, the standard form of a number can be used for any number that can be expressed as a decimal and multiplied by the appropriate power of 10.

Why is this concept useful?

Accurately displaying the standard form of a number is useful in manipulating larger and smaller quantities with ease and is especially useful to scientists as it allows for ordering amounts, quantifying amounts, and making predictions. Converting -in and out of- standard form is an essential skill in chemistry and in the sciences, in general.

Where does this concept fit into the curriculum?

Grade 8

How can we use the concept:

One real world example of standard form is expressing the speed of light in standard form. The speed of light is [299 792 458 m/s or approximately 300,000,000]. Shown in standard form the speed of light is [3 x 10⁸].

Sample Math Problems

1. Write 6.351 x 10⁷ (standard form)

Answer: [63,510,000]

Explanation: Since the decimal is located after the 6 and there are 3 spaces after the decimal, move the decimal 7 spaces to the right adding 4 zeros to fill in the spaces.

A positive exponent signals moving the decimal in the right-hand direction.

Therefore, [63,510,000] is the answer. In this whole number the decimal is “understood” to be behind the number but is not expressed in the solution.

2. Write

4.806 x 10−144.806\ x\ 10^{-14}

(standard form)

Answer: [.00000000000004806]

Explanation: Since the decimal is located after the 4 and there are 3 spaces after the decimal, move the decimal 14 spaces to the left adding 13 zeros to fill in the spaces.
A negative exponent signals moving the decimal in the left-hand direction.
Therefore, [.00000000000004806] is the answer.


3. Write

6.37 x 10−66.37\ x\ 10^{-6}

Answer: [.00000637]

Explanation: Since the decimal is located after the 6 and there are 2 spaces after the decimal, move the decimal 6 spaces to the left and add 5 zeros to fill the spaces.

A negative exponent signals moving the decimal in the left-hand direction.

Therefore, [.00000637] is the answer.


4. Write

8.4 x 1058.4\ x\ 10^{5}

Answer: [840,000]

Explanation: Since the decimal is located after the 8 and there is 1 space after the decimal, move the decimal 5 spaces to the right adding in 4 zeros in the spaces.

A positive exponent signals moving the decimal in the right-hand direction.


Therefore, [840,000] is the answer. In this whole number the decimal is “understood” to be behind the number but is not expressed in the solution.

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Practice Math Problems

1. Write

4.567 x 1084.567\ x\ 10^{8}

2. Write

8.56 x 10−108.56\ x\ 10^{-10}

3. Write

4389.34 x 1034389.34\ x\ 10^{3}

4. Write

567.89 x 10−4567.89\ x\ 10^{-4}

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