Decimal numbers have places to the right of the decimal point. Each position represents a different fraction of a whole. In the number 1.234, we have the ones place, then the decimal point, followed by tenths, hundredths, and thousandths. The digit 2 is in the tenths place, 3 is in the hundredths place, and 4 is in the thousandths place.
Now let's analyze the number 0.078. We can see that 0 is in the ones place, 0 is in the tenths place, 7 is in the hundredths place, and 8 is in the thousandths place. The digit 7 is in the hundredths place, which means its value is related to 1/100 or 0.01.
The hundredths place represents 1/100 or 0.01 of a whole. We can visualize this with a 10 by 10 grid, which has 100 equal parts. If we shade 7 of these parts, we have 7 hundredths. Mathematically, this is 7 times 1/100, which equals 7/100 or 0.07.
The value of 7 in 0.078 can be expressed in multiple ways. As a fraction, it's 7/100. As a decimal, it's 0.07. In expanded form, it's 7 times 10 to the power of negative 2. In words, we say seven hundredths. Let's compare this with other decimal places. 0.7 is seven tenths, 0.07 is seven hundredths, and 0.007 is seven thousandths. The position of the digit determines its value.
Let's practice with more examples. First, what is the value of 3 in 0.345? The 3 is in the tenths place, so its value is 3 times 1/10, which equals 3/10 or 0.3. Second, what is the value of 9 in 0.092? The 9 is in the hundredths place, so its value is 9 times 1/100, which equals 9/100 or 0.09. Third, what is the value of 6 in 0.506? The 6 is in the thousandths place, so its value is 6 times 1/1000, which equals 6/1000 or 0.006. To summarize, in the number 0.078, the digit 7 has a value of 7 hundredths or 0.07.