Multiplying Tenths to Get Hundredths
Multiplying Tenths to Get Hundredths is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) that teaches students that 0.1 × 0.1 = 0.01, and more generally that multiplying a tenths-place decimal by another tenths-place decimal produces a result in the hundredths place. This mirrors fraction multiplication (1/10 × 1/10 = 1/100) and is foundational for understanding how place values shift in decimal multiplication.
Key Concepts
Property When you multiply a number in the tenths place by another number in the tenths place, the product will be in the hundredths place. $$0.1 \times 0.1 = 0.01$$ $$\frac{1}{10} \times \frac{1}{10} = \frac{1}{100}$$.
Examples $0.2 \times 0.4 = 0.08$ $0.7 \times 0.3 = 0.21$ $1.5 \times 0.2 = 0.30$ or $0.3$.
Explanation Multiplying tenths by tenths is similar to multiplying fractions. For example, $0.2 \times 0.4$ is the same as $\frac{2}{10} \times \frac{4}{10}$, which equals $\frac{8}{100}$, or $0.08$. A general rule is to multiply the numbers as if they were whole numbers, and then count the total number of decimal places in the factors to place the decimal in the product. This skill is foundational for understanding how place values shift during decimal multiplication.
Common Questions
What do you get when you multiply two tenths together?
Multiplying two numbers in the tenths place produces a number in the hundredths place. For example, 0.2 × 0.4 = 0.08, and 0.7 × 0.3 = 0.21. The rule is 0.1 × 0.1 = 0.01.
Why does multiplying tenths give hundredths?
Because (1/10) × (1/10) = 1/100. Multiplying two tenths means multiplying two fractions with denominator 10, giving a fraction with denominator 100, which is hundredths.
What chapter covers multiplying tenths in Illustrative Mathematics Grade 5?
Multiplying tenths to get hundredths is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.
How do you multiply decimals in the tenths place?
Multiply the digits as if they were whole numbers, then count the total decimal places in both factors. Each tenths-place factor has one decimal place, so the product has two decimal places (hundredths).
What is an example of multiplying tenths to get hundredths?
0.7 × 0.3 = 0.21. Treat as 7 × 3 = 21, then since each factor has 1 decimal place, the product has 2 decimal places: 0.21. Another example: 1.5 × 0.2 = 0.30, since 15 × 2 = 30 and there are 2 total decimal places.