Scientific Notation: Homework

One digit in front of the point, then a power of ten. Count the moves and you have the exponent.

Part A — Convert / 10

For 1 to 5, write the number in scientific notation. For 6 to 10, write it in standard form.

Each of these has a trap. Check that the first number is at least 1 and less than 10.

1.
Is 45 × 10^3 in scientific notation? If not, rewrite it.Answer
2.
Write 0.6 × 10^5 in scientific notation.Answer
3.
Write 7,000,000 in scientific notation. Count the zeros carefully.Answer
4.
Which is greater, 9.9 × 10^4 or 1.1 × 10^5? The first has the bigger front number.Answer
5.
Write 6.2 × 10^1 as a plain number.Answer

Real numbers, rounded to make them easy to write: the speed of light and the light-year, and census counts of the people in the United States.

Fact	Number
Speed of light, meters per second	300,000,000
One light-year, kilometers	9,460,000,000,000

Think it through, then write your answer and one sentence about how you knew.

1.
Put these in order from least to greatest without writing them in standard form: 4.2 × 10^6, 9.1 × 10^5, 4.15 × 10^6, 1.0 × 10^7. Tell what you compared first.Answer
2.
The number 6.5 × 10^k is between 1,000,000 and 10,000,000. What is k? Write the number out to check.Answer

Write your own, then work it.

1.
Pick a big number you know about, such as a distance, a population or a count of something. Write it rounded in standard form and in scientific notation, and say how many places the point moved.Answer

Total / 24

Graded by

Notes

Part A — the converted numbers.

Part B — the answer.

4.5 × 10^4. It was not in scientific notation, because 45 is not between 1 and 10.
6 × 10^4. 0.6 × 100,000 is 60,000, and the 6 needs to be in the ones place.
7 × 10^6. There are six zeros.
1.1 × 10^5 is greater. 99,000 is less than 110,000, so compare the exponents first.
62. An exponent of 1 moves the point one place.

Part C — the answers.

a. 3 × 10^8 b. 9.46 × 10^12 c. 31,536,000 seconds, which is about 3.15 × 10^7
a. 1.51 × 10^8, 3.31 × 10^8 and 8 × 10^9 b. 1.51 × 10^8 < 3.31 × 10^8 < 8 × 10^9 c. 180,000,000, or 1.8 × 10^8

Part D — one correct answer, and what a good explanation says.

9.1 × 10^5 < 4.15 × 10^6 < 4.2 × 10^6 < 1.0 × 10^7. Compare the exponents first. The two with 10^6 tie, so compare the front numbers, 4.15 and 4.2.
6. 6.5 × 10^6 = 6,500,000, which is between the two.

Part E — what a good problem looks like.

Answers vary. A good one rounds first and counts the moves, such as 24,000,000 = 2.4 × 10^7, where the point moved seven places.