The number 0.960 is larger than the number 0.0962.
The correct answer and explanation is:
The statement is true. The number 0.960 is indeed larger than 0.0962.
To compare these two numbers, it’s useful to look at the place value of each digit. Both numbers have a decimal point, so we will start by comparing the digits from left to right.
For 0.960, the digits are as follows:
- The first digit after the decimal point is 9 in the tenths place.
- The second digit is 6 in the hundredths place.
- The third digit is 0 in the thousandths place.
For 0.0962, the digits are:
- The first digit after the decimal point is 0 in the tenths place.
- The second digit is 9 in the hundredths place.
- The third digit is 6 in the thousandths place.
- The fourth digit is 2 in the ten-thousandths place.
Comparing the first place after the decimal point, 9 in 0.960 is clearly greater than 0 in 0.0962, making 0.960 larger right away. Even though the numbers look similar after the decimal point, the fact that 0.960 has a 9 in the tenths place and 0.0962 has only a 0 there gives a large difference in their overall value.
Even if we continued to look further at the hundredths, thousandths, and ten-thousandths places, the digits of 0.0962 do not surpass those of 0.960 in any place value. Thus, 0.960 is greater than 0.0962.
In conclusion, understanding place value is crucial for comparing decimal numbers. The larger digits in the more significant places (the tenths in this case) lead to a larger overall number.