Let's solve the question step by step:
### Part (a)
Approximate the width of the smartphone by rounding to the nearest hundredth of a meter:
The given width of the smartphone is 0.0710 meters. To round this number to the nearest hundredth, we look at the digit in the thousandth place (which is the third digit to the right of the decimal point).
- If the digit in the thousandth place is 5 or greater, we round the hundredth place up by one.
- If the digit in the thousandth place is less than 5, we leave the hundredth place as it is.
In this case, the thousandth place digit is 1, which is less than 5. Therefore, we keep the hundredth place the same and round down.
Thus, the width of the smartphone rounded to the nearest hundredth is:
[tex]\[ \boxed{0.07} \][/tex]
### Part (b)
Write the answer from part (a) as a single digit times a unit fraction with a denominator written as a power of 10 in exponential form:
The answer from part (a) is 0.07 meters. First, let's express 0.07 as a fraction:
[tex]\[ 0.07 = \frac{7}{100} \][/tex]
Now, we need to write this fraction as a single digit times a unit fraction (a fraction with a numerator of 1) with the denominator as a power of 10.
In the fraction [tex]\( \frac{7}{100} \)[/tex]:
- The numerator is 7, which is the single digit.
- The denominator is 100, which we can write as [tex]\( 10^2 \)[/tex] (since 100 is [tex]\( 10^2 \)[/tex]).
Therefore, we can express the given width as:
[tex]\[ 7 \times \frac{1}{100} \quad \text{or} \quad 7 \times \frac{1}{10^2} \][/tex]
So, the answer is:
[tex]\[ \boxed{7 \times \frac{1}{10^2}} \][/tex]
