Question

What is the greatest degree of precision to which the metal bar can be measured by ruler A and by ruler B? A) to the nearest tenth by both rulers

B) to the nearest hundredth by both rulers
C) to the nearest tenth by ruler A and to the nearest
hundredth by ruler B
D) to the nearest hundredth by ruler A and to the
nearest tenth by ruler B

Answer 1

The greatest degree of precision for ruler A and ruler B is to the nearest tenth, to the nearest hundredth, or a combination of both.

Step-by-step explanation:

The greatest degree of precision to which the metal bar can be measured by ruler A and ruler B is as follows:

1. A) to the nearest tenth by both rulers: In this case, both rulers can measure the length of the metal bar to the nearest tenth, which means that the measurement can have one decimal digit after the decimal point, like 2.5 cm or 3.6 cm.
2. C) to the nearest tenth by ruler A and to the nearest hundredth by ruler B: Here, ruler A can measure the length to the nearest tenth, while ruler B can measure it to the nearest hundredth. This means that the measurement can have one decimal digit after the decimal point with ruler A, and two decimal digits after the decimal point with ruler B, like 2.3 cm or 2.34 cm.
3. D) to the nearest hundredth by ruler A and to the nearest tenth by ruler B: In this case, ruler A can measure the length to the nearest hundredth, while ruler B can only measure it to the nearest tenth. So, the measurement can have two decimal digits after the decimal point with ruler A, and one decimal digit after the decimal point with ruler B, like 2.36 cm or 2.5 cm.

Answer 2

The metal bar can be measured to the nearest tenth of a centimeter by Ruler B and to the nearest hundredth of a centimeter by Ruler A, making option C the correct choice.

Step-by-step explanation:

The greatest degree of precision to which the metal bar can be measured by Ruler A and by Ruler B is related to the smallest increments each ruler can measure. Ruler A can measure to the nearest hundredth because it has markings for tenths of a centimeter and allows the user to estimate to the hundredths. On the other hand, Ruler B, with centimeter and millimeter markings, provides measurements to the nearest tenth of a centimeter (millimeter).

Therefore, Ruler A gives a measurement that can be rounded to 2.55 cm, indicating two certain digits (2 and 5) and one estimated (hundredths place), whereas Ruler B's measurement of 2.5 cm has only one certain digit, the whole number (2), and one estimated (the tenths place).

Basing on the precision of measuring tools and significant figures, the correct answer is option C: to the nearest tenth by Ruler A and to the nearest hundredth by Ruler B.