Write the following as a sum using powers of 10 to show place value and explain your steps.
3) 620.83
To write 620.83 as a sum using powers of 10, we need to break down the number by its place values.
First, let's identify the place value of each digit in the number.
6: This digit is in the hundreds place, which means it represents 6 hundreds, or 600.
2: This digit is in the tens place, which means it represents 2 tens, or 20.
0: This digit is in the ones place, which means it represents 0 ones.
. : This is the decimal point, separating the whole number part from the fractional part.
Moving to the right of the decimal point:
8: This digit is in the tenths place, which means it represents 8 tenths, or 0.8.
3: This digit is in the hundredths place, which means it represents 3 hundredths, or 0.03.
Now, let's write 620.83 as a sum:
620 = 6 × 100 = 6 × 10²
20 = 2 × 10 = 2 × 10¹
0 = 0 × 1 = 0 × 10⁰
0.8 = 8 × 0.1 = 8 × 10⁻¹
0.03 = 3 × 0.01 = 3 × 10⁻²
Combining these values, we can write 620.83 as the sum of its place values using powers of 10:
620.83 = (6 × 10²) + (2 × 10¹) + (0 × 10⁰) + (8 × 10⁻¹) + (3 × 10⁻²)
So, 620.83 can be expressed as the sum of its place values using powers of 10.