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Relate tenths to fractions and decimals

A tenth is one of ten equal parts of a whole, represented as 110\frac{1}{10} and 0.10.1; quantities of several tenths can be represented equivalently as fractions with denominator 10, decimals, and points on a number line. This understanding connects the tenths place to base-ten place value and supports comparing and composing numbers such as 2.32.3, without extending to hundredths or more general decimal expansions.

Detailed Explanation: Relate tenths to fractions and decimals

A tenth is one of 10 equal parts of a whole.

one tenth=110=0.1\text{one tenth}=\frac{1}{10}=0.1

Each additional tenth adds another (0.1)(0.1).

Example: Represent 2 wholes and 3 tenths.

  1. There are 22 whole units and 33 tenths.
  2. Write the amount as a fraction:
23102\frac{3}{10}

The 33 in the numerator means 3 tenths.

  1. Write the amount as a decimal. The tenths digit goes immediately to the right of the decimal point:
2.32.3

So,

2310=2.32\frac{3}{10}=2.3
  1. To show (2.3)(2.3) on a number line, look between 22 and 33. Divide that space into 10 equal parts. Each step is one tenth:
2, 2.1, 2.2, 2.3, 2.4,…,32,\ 2.1,\ 2.2,\ \boxed{2.3},\ 2.4,\ldots,3

The point for (2.3)(2.3) is the third tenth after 22. Thus, (2.3)(2.3) means 2 wholes and 3 tenths.

Learn by doing: Relate tenths to fractions and decimals

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    Decimal Concept Image - Decimal to Picture and Fraction (10s) - Tenths

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