Answer
a) $6.5 * 10^{2}$
b) $6.30 * 10^{-2} $
c) $86 * 10^2$
d) $8.6*10^3$
e) $1.6*10^4$
f) $1.00010 * 10^{-1}$
Work Step by Step
a) Scientific notation required us to write the number using a power of 10 and a decimal number between 1 and 10. To write 650 with a decimal between 1 and 10, we must write it as 6.5. Since we moved the decimal point over 2 places to the left, the power of 10 is positive 2.
b) To write 0.0630 with a decimal between 1 and 10, we must write it as 6.3. Since we moved the decimal place two places to the right, the power of 10 is negative 2.
c) Here, the problem specifies that we measured the number to 10, which means the scientific notation needs to have a tens place. Writing 8600 in the tens place gives us 86. Since we moved the decimal point two to the left, the power of 10 is positive 2.
d) To write 8600 with a decimal between 1 and 10, we must write it as 8.6. Since we moved the decimal three places to the left, the power of 10 is positive 3.
e) To write 16000 with a decimal between 1 and 10, we must write it as 1.6. Since we moved the decimal four places to the left, the power of 10 is positive 4.
f) To write 0.100010 with a decimal between 1 and 10, we must write it as 1.00010. Since we moved the decimal place once to the right, the power of 10 is negative 1.
