Every digit in a number has a particular place value depending on its location within the number. For example, in the number 452, the digit 2 is in the ones (or “units”) place, the digit 5 is in the tens place, and the digit 4 is in the hundreds place. The name of each location corresponds to the “value” of that place. Thus:
2 is worth two “units” (two “ones”), or 2 (= 2 × 1).
5 is worth five tens, or 50 (= 5 × 10).
4 is worth four hundreds, or 400 (= 4 × 100).
You can now write the number 452 as the sum of these products:
452 = (4 × 100) + (5 × 10) + (2 × 1)
(“four hundreds plus five tens plus two ones”)
The chart shown analyzes the place value of all the digits in the number:
692,567,891,023.8347
Notice that the place values to the left of the decimal all end in “-s,” while the place values to the right of the decimal all end in “-ths.” This is because the suffix “-ths” gives these places (to the right of the decimal) a fractional value.
Now analyze the end of the preceding number: 0.8347
The 8 is in the tenths place, giving it a value of 8 tenths, or
.
The 3 is in the hundredths place, giving it a value of 3 hundredths or
.
The 4 is in the thousandths place, giving it a value of 4 thousandths, or
.
The 7 is in the ten-thousandths place, giving it a value of 7 ten-thousandths, or
.
To use a concrete example, 0.8 might mean eight-tenths of one dollar, which would be 8 dimes, or 80 cents. Additionally, 0.03 might mean three-hundredths of one dollar, which would be 3 pennies, or 3 cents.
How many digits are in 99,999?
In the number 4,472.1023, in what place value is the 1?