Question

convert each of the following numbers from scientific to ord and write its name.
a. 5×10²
b. 6.1×10³
c. 7×10⁻⁶
d. 4.5×10⁻⁴
a. 5×10² = 500 = five hundred (type an integer or a decimal.)
b. 6.1×10³ = 6100 = six thousand one hundred (type an integer or a decimal.)
c. 7×10⁻⁶ = 0.000007 = seven millionths (type an integer or a decimal.)
d. 4.5×10⁻⁴ = 0.00045 = forty - five ten - thousandths (type an integer or a decimal.)

Explanation:

Step1: Recall scientific - notation rule for positive exponents

For \(a\times10^{n}\) where \(n>0\), move the decimal point \(n\) places to the right. For \(5\times 10^{2}\), \(n = 2\), so \(5\times10^{2}=5\times100 = 500\), named five hundred.

Step2: Apply rule for \(6.1\times10^{3}\)

Since \(n = 3\) in \(6.1\times10^{3}\), move the decimal point 3 places to the right. \(6.1\times10^{3}=6.1\times1000=6100\), named six thousand one hundred.

Step3: Recall scientific - notation rule for negative exponents

For \(a\times10^{-n}\) where \(n>0\), move the decimal point \(n\) places to the left. For \(7\times10^{-6}\), move the decimal point 6 places to the left, getting \(0.000007\), named seven millionths.

Step4: Apply rule for \(4.5\times10^{-4}\)

For \(4.5\times10^{-4}\), move the decimal point 4 places to the left, getting \(0.00045\), named forty - five ten - thousandths.

Answer:

a. \(500\), five hundred
b. \(6100\), six thousand one hundred
c. \(0.000007\), seven millionths
d. \(0.00045\), forty - five ten - thousandths