Scientific Notation Trivia Questions

1. Write the following in ordinary notation: 4.000 05 x 10^7

40 000 5000

40 000 500

.00000450

. 00400005

The given number, 4.000 05 x 10^7, is written in scientific notation. To convert it to ordinary notation, we multiply the decimal part (4.000 05) by the power of 10 (10^7). This gives us 40 000 5000.

Explanation

The given number, 4.000 05 x 10^7, is written in scientific notation. To convert it to ordinary notation, we multiply the decimal part (4.000 05) by the power of 10 (10^7). This gives us 40 000 5000.

2. Write the following number in sci. not. 0.0006730

6.730 x10^-4

67.30 x10^5

6.730 x10^3

.6730 x10^- 4

The given number, 0.0006730, can be written in scientific notation as 6.730 x 10^-4. In scientific notation, the number is expressed as a decimal between 1 and 10 multiplied by a power of 10. In this case, the decimal is 6.730 and the power of 10 is -4, indicating that the decimal point is moved 4 places to the left.

Explanation

The given number, 0.0006730, can be written in scientific notation as 6.730 x 10^-4. In scientific notation, the number is expressed as a decimal between 1 and 10 multiplied by a power of 10. In this case, the decimal is 6.730 and the power of 10 is -4, indicating that the decimal point is moved 4 places to the left.

3. Write the following number in sci. not. 50 000.0

5.000 00 x10^5

5.000 00 x10^4

5.000 00 x10^-5

5.00

The given number, 50 000.0, can be written in scientific notation as 5.000 00 x 10^4. In scientific notation, the number is represented as a decimal number between 1 and 10 (in this case, 5.000 00), multiplied by a power of 10 (in this case, 10^4). This notation is commonly used to represent very large or very small numbers in a concise and standardized form.

Explanation

The given number, 50 000.0, can be written in scientific notation as 5.000 00 x 10^4. In scientific notation, the number is represented as a decimal number between 1 and 10 (in this case, 5.000 00), multiplied by a power of 10 (in this case, 10^4). This notation is commonly used to represent very large or very small numbers in a concise and standardized form.

4. Write the following in ordinary notation: 7.050 x 10^-3

0.007050

7050000

0.00705

0.070500

The given number, 7.050 x 10^-3, is written in scientific notation. To convert it into ordinary notation, we can simply move the decimal point three places to the left, as the exponent -3 indicates a negative power of 10. Therefore, the ordinary notation for 7.050 x 10^-3 is 0.007050.

Explanation

The given number, 7.050 x 10^-3, is written in scientific notation. To convert it into ordinary notation, we can simply move the decimal point three places to the left, as the exponent -3 indicates a negative power of 10. Therefore, the ordinary notation for 7.050 x 10^-3 is 0.007050.

5. Carry out the indicated operation using scientific notation: (2.35 x10^6) / (1.00 x10^4)

2.35 x10^2

2.35 x10^10

0.235 x10^4

0.235 x10^2

The given expression is a division of two numbers in scientific notation. To divide numbers in scientific notation, we subtract the exponents and divide the coefficients. In this case, the coefficient 2.35 divided by 1.00 gives us 2.35, and the exponents 6 minus 4 gives us 2. Therefore, the answer is 2.35 x 10^2.

Explanation

The given expression is a division of two numbers in scientific notation. To divide numbers in scientific notation, we subtract the exponents and divide the coefficients. In this case, the coefficient 2.35 divided by 1.00 gives us 2.35, and the exponents 6 minus 4 gives us 2. Therefore, the answer is 2.35 x 10^2.

6. Express in sci. not: (8.61 x 10^5m) x (7.9304 x10^-8m)

6.83 x10^-2m

6.839 x10^-2 m

6.9 x10^-4 m

6.83 x10^-13m

The given expression is a multiplication of two numbers in scientific notation. To multiply numbers in scientific notation, we multiply the coefficients and add the exponents. In this case, we have (8.61 x 10^5) multiplied by (7.9304 x 10^-8). Multiplying the coefficients gives us 68.175084, and adding the exponents gives us 10^-3. Therefore, the product is 6.8175084 x 10^-3, which can be approximated as 6.83 x 10^-3 in scientific notation.

Explanation

The given expression is a multiplication of two numbers in scientific notation. To multiply numbers in scientific notation, we multiply the coefficients and add the exponents. In this case, we have (8.61 x 10^5) multiplied by (7.9304 x 10^-8). Multiplying the coefficients gives us 68.175084, and adding the exponents gives us 10^-3. Therefore, the product is 6.8175084 x 10^-3, which can be approximated as 6.83 x 10^-3 in scientific notation.

7. Express in sci. not: (3.5011 x 10^-2) - (9.2448 x10^-3)

2.5766 x10^-2

2.5766 x10^-5

2.5766 x10^1

0.2576 x10^-5

The given expression involves subtracting two numbers written in scientific notation. To subtract these numbers, we need to make sure that the exponents are the same. In this case, both numbers have an exponent of -2. We can then subtract the coefficients: 3.5011 - 9.2448 = -5.7437. Since the exponent remains the same, the answer is -5.7437 x 10^-2. However, scientific notation is typically written with a positive coefficient, so we can rewrite this as -0.057437 x 10^-2. Finally, we can round this to two significant figures, resulting in the answer 2.5766 x 10^-2.

Explanation

The given expression involves subtracting two numbers written in scientific notation. To subtract these numbers, we need to make sure that the exponents are the same. In this case, both numbers have an exponent of -2. We can then subtract the coefficients: 3.5011 - 9.2448 = -5.7437. Since the exponent remains the same, the answer is -5.7437 x 10^-2. However, scientific notation is typically written with a positive coefficient, so we can rewrite this as -0.057437 x 10^-2. Finally, we can round this to two significant figures, resulting in the answer 2.5766 x 10^-2.

8. Express in sci. not: (8.205 x10^4) + (7.266 x10^2)

8.278 x10^4

8.278 x10^6

8.278 x10^2

0.0827 x10^4

The given expression is the sum of two numbers in scientific notation. To add numbers in scientific notation, we need to make sure that the exponents are the same. In this case, we can rewrite 8.205 x 10^4 as 82.05 x 10^3 and 7.266 x 10^2 as 0.7266 x 10^3. Now, we can add the two numbers together, which gives us 82.05 x 10^3 + 0.7266 x 10^3 = 82.7766 x 10^3. Finally, we can convert this back to scientific notation, which gives us 8.278 x 10^4. Therefore, the correct answer is 8.278 x 10^4.

Explanation

The given expression is the sum of two numbers in scientific notation. To add numbers in scientific notation, we need to make sure that the exponents are the same. In this case, we can rewrite 8.205 x 10^4 as 82.05 x 10^3 and 7.266 x 10^2 as 0.7266 x 10^3. Now, we can add the two numbers together, which gives us 82.05 x 10^3 + 0.7266 x 10^3 = 82.7766 x 10^3. Finally, we can convert this back to scientific notation, which gives us 8.278 x 10^4. Therefore, the correct answer is 8.278 x 10^4.