Divide the following decimals mentally. 1. 2.3 divide 0.1 2. 76.563 divide 0.001 3. 6.56 divide 0.01
The correct answer and explanation is:
Correct Answers:
- 2.3 ÷ 0.1 = 23
- 76.563 ÷ 0.001 = 76,563
- 6.56 ÷ 0.01 = 656
Explanation:
To divide decimals mentally, it helps to understand how dividing by a decimal affects the number. Dividing by a number less than one increases the original number. This happens because smaller divisors fit into a number more times.
When dividing a decimal by a power of ten (such as 0.1, 0.01, or 0.001), you can move the decimal point to the right by the number of zeros in the divisor.
- 2.3 ÷ 0.1:
Dividing by 0.1 means you are finding how many tenths fit into 2.3.
Move the decimal point one place to the right: 2.3 becomes 23.
So, 2.3 ÷ 0.1 = 23. - 76.563 ÷ 0.001:
Dividing by 0.001 means you are finding how many thousandths fit into 76.563.
Move the decimal point three places to the right: 76.563 becomes 76,563.
So, 76.563 ÷ 0.001 = 76,563. - 6.56 ÷ 0.01:
Dividing by 0.01 means you are finding how many hundredths fit into 6.56.
Move the decimal point two places to the right: 6.56 becomes 656.
So, 6.56 ÷ 0.01 = 656.
Understanding this mental math method helps to quickly handle division problems involving decimals. Rather than using long division, shifting the decimal point is a faster and more intuitive way. This method relies on recognizing the pattern and using place value knowledge to simplify the calculation. It is especially useful in daily tasks like converting money or measuring units.