Math Lesson 7.3.2 - Writing Decimals in Standard and Decomposed Form

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Welcome to our Math lesson on Writing Decimals in Standard and Decomposed Form, this is the second lesson of our suite of math lessons covering the topic of Standard Form, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Writing Decimals in Standard and Decomposed Form

In tutorial 3.5 we discussed decimals as an alternative form to fractions for expressing the non-whole numbers. In that tutorial, we explained that a decimal is composed by three parts: a group of digits on the left, which represent the whole part of the number, another group of digits on the right that represents the non-whole part and a decimal point that separates the whole and non-whole parts.

We can extend the reasoning used for numbers written in standard form beyond the decimal point to also include the decimal numbers. This can be easily done now that you are familiar with negative indices. Thus, a decimal that is written in the form

(where abcd is the whole part while efgh is the decimal part) can be expressed in the decomposed form as

In other words, we have

When written in the standard form, this number becomes

For example, 32.7 is written in the standard form as

Example 2

Write the following decimals in the standard form.

1. 106.24
2. 3.089

Solution 2

1. We have
   106.24 = 1 × 10² + 0 × 10¹ + 6 × 10⁰ + 2 × 10^-1 + 4 × 10^-2
   = 1.0624 × 10²
2. 3.089 = 3 × 10⁰ + 0 × 10^-1 + 8 × 10^-2 + 9 × 10^-3
   = 3.089 × 10⁰

More Standard Form Lessons and Learning Resources

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Enjoy the "Writing Decimals in Standard and Decomposed Form" math lesson? People who liked the "Standard Form lesson found the following resources useful:

1. Decimals Feedback. Helps other - Leave a rating for this decimals (see below)
2. Powers and Roots Math tutorial: Standard Form. Read the Standard Form math tutorial and build your math knowledge of Powers and Roots
3. Powers and Roots Video tutorial: Standard Form. Watch or listen to the Standard Form video tutorial, a useful way to help you revise when travelling to and from school/college
4. Powers and Roots Revision Notes: Standard Form. Print the notes so you can revise the key points covered in the math tutorial for Standard Form
5. Powers and Roots Practice Questions: Standard Form. Test and improve your knowledge of Standard Form with example questins and answers
6. Check your calculations for Powers and Roots questions with our excellent Powers and Roots calculators which contain full equations and calculations clearly displayed line by line. See the Powers and Roots Calculators by iCalculator™ below.
7. Continuing learning powers and roots - read our next math tutorial: Surds

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