Final answer:
The width seven hundred two thousandths of a meter is expressed as a fraction 351/500 and as a decimal in expanded form as 0.7 + 0.00 + 0.002. Measurements should be as precise as the instrument used allows.
Step-by-step explanation:
The student measured the width of a desk to be seven hundred two thousandths of a meter. To write this measurement as a fraction, you would use the number of thousandths as the numerator and 1000 as the denominator, which is 702/1000. To simplify this fraction, we can divide both the numerator and the denominator by 2 to get 351/500.
To express the measurement in decimal form, write it out as 0.702. The expanded form of this decimal is 7/10 + 0/100 + 2/1000, which literally expands the number into its place value components.
It is essential to understand the precision of measuring instruments; measurements should only be reported to the highest degree of precision that the measuring device allows. Since the fraction and expanded decimal form represent the same value, it is important to match the precision of the actual measurement with the precision of the reporting units.