Exam 5: Using Numbers in Sensible Ways

Using benchmarks, what is the BEST estimate of the time it would take, averaging 50 mph for 8 hours a day, to drive across the United States (about 3000 miles)?

Company X bought 17,569 truckloads worth $24,598 each. Company Y bought 24,598 truckloads worth $17,569 each. Which company paid more?

Using benchmarks, find an estimate of each calculation and explain your reasoning. A) 7.5% of $594 B) 0.32147 × (67.557% of 89.4853) C) $2 \frac { 8 } { 9 } + \left( \frac { 13 } { 24 } \times 0.99184 \right)$ D) 5.8 ÷ 12

Write in scientific notation. A) 38,000,000,000 B) 382.45 C) 0.000 000 000 456

1.334496 × 301.66 is CLOSEST to:

278.4132987 × 0.2617944285 is about:

Is 40 ÷ 1.99 less than, equal to, or greater than 20? Explain, showing your understanding of a meaning of division.

Why is this student NOT showing good number sense in estimating 249.738 + 48.246? "Well, 249 is about 250, and 48 is about 50. 250 + 50 is 300. Then .738 + .246 is about 1. So, my estimate is 301."

Kyle estimated that 23 × 31 was 603. Use a rectangular area model to illustrate the misunderstanding and the correct product.

Give the exact answer by mental calculation, and then write down your thinking. You are asked for a second way of thinking in parts B and C. A) 479.38 + 18.9 + 2.4 - 479.38 = _____ B) 12 × 125 = _____ (Give two ways for part B.) C) 1714 - 897 = _____ (Give two ways for part C.) D) 20% of 45 = _____

Give the exact answer mentally: 73.8 + 511.37 + 24 - 73.8. Describe your thought process.

For each calculation, mentally obtain an estimate of the answer and write it in the blank. Use number sense. Then write enough to make your thought process clear. A) 34% discount on an $89 suitcase _____ B) 0.26 × 43,135 ? _____ C) 61 × 334 ?_____ D) 74.35% × 1195 × 0.9837 ? _____ E) (1201.794 ÷ 0.25) + 0.0423 ?_____

You are using a calculator that can show only eight digits of an answer. When you finish, you realize that you forgot to press the decimal points in the original numbers. Show where the decimal points go and explain how you know, using number sense (no paper-pencil calculation). A) 9.87429 × 637.21945 = 6 2 9 2 0 8 9 6 B) 413.69824 ÷ 24.92617 = 1 6 5 9 6 9 4 4

How many seconds does it take light to reach the Earth from the sun? Express your answer in scientific notation. (The Earth is 150,000,000,000 meters from the sun, and the speed of light is 300,000,000 meters per second.)

0.7614987 × 159.23842 is about:

Use number sense in locating the decimal point in the answer. Explain your thinking briefly. A) 77.5 × 2.84 = 2 2 0 1 B) 1002.6 ÷ 3.6 = 2 7 8 5

Write each value in scientific notation. A) The Earth is 150,000,000,000 meters from the sun. B) The speed of light is 300,000,000 meters per second. C) A dust particle is 0.000 000 000 753 kg.

Determine each calculation mentally, writing enough to make your mental work clear. A) 40% of 80 B) 15% of 300 C) 20% of 14 D) 100% of 71 E) 5% of 60 F) 120% of 20 G) 15 is 25% of ? H) 14 is 50% of ?