How are the decimals 0.009 and 0.09 related? Explain.
The correct answer and explanation is:
Correct Answer:
The decimal 0.009 is one-tenth of 0.09, or 0.009 = 0.09 ÷ 10.
300-Word Explanation:
Decimals represent parts of a whole and are based on powers of ten. To understand the relationship between 0.009 and 0.09, we must examine their place values.
- 0.09 means 9 hundredths. It has a 9 in the hundredths place (second digit to the right of the decimal point).
This can be written as a fraction: 0.09=91000.09 = \frac{9}{100} - 0.009 means 9 thousandths. It has a 9 in the thousandths place (third digit to the right of the decimal point).
This can be written as a fraction: 0.009=910000.009 = \frac{9}{1000}
Now compare these two: 91000÷9100=110\frac{9}{1000} \div \frac{9}{100} = \frac{1}{10}
So, 0.009 is one-tenth of 0.09. In decimal terms: 0.09÷10=0.0090.09 \div 10 = 0.009
Or going the other direction: 0.009×10=0.090.009 \times 10 = 0.09
This shows a scaling relationship: multiplying or dividing by 10 moves the digits one place value to the left or right. In this case, since 0.009 is one place value smaller, it is ten times smaller than 0.09.
This understanding is crucial in math because it helps when comparing decimal numbers or converting between forms. Students often confuse which number is larger when they see more digits. However, more digits after the decimal point do not mean the number is larger. In fact, 0.009 is less than 0.09, despite having more digits, because the nonzero digit is further to the right.
Conclusion:
0.009 is one-tenth of 0.09, and this can be proven by comparing place values, using fractions, and applying multiplication or division by 10.