What decimal represents each number?

Mathematics · Middle School · Mon Jan 18 2021

Answered on

To represent a number as a decimal, you need to express it in terms of powers of ten. In a decimal number system, each position represents a successive power of ten. For example, the number "345" is a decimal number and is interpreted as follows:

- The "5" is in the ones place, which is \( 10^0 \) (since any number to the power of 0 is 1). So, 5 represents \( 5 \times 10^0 \), which is 5. - The "4" is in the tens place, which is \( 10^1 \). So, 4 represents \( 4 \times 10^1 \), which is 40. - The "3" is in the hundreds place, which is \( 10^2 \). So, 3 represents \( 3 \times 10^2 \), which is 300.

Thus, the number 345 is actually \( 300 + 40 + 5 \) in decimal form.

For another example, in the number "78.09":

- The "7" is in the tens place, which is \( 10^1 \). So, 7 represents \( 7 \times 10^1 \), which is 70. - The "8" is in the ones place, which is \( 10^0 \). So, 8 represents \( 8 \times 10^0 \), which is 8. - The "0" is in the tenths place, which is \( 10^{-1} \). So, 0 represents \( 0 \times 10^{-1} \), which is 0. - The "9" is in the hundredths place, which is \( 10^{-2} \). So, 9 represents \( 9 \times 10^{-2} \), which is 0.09.

Adding these up gives us \( 70 + 8 + 0 + 0.09 \), hence the number 78.09 in decimal form.

If you have specific numbers in mind, please provide them and I can give you the decimal representation for those.