1. Which is larger? 2.75 x 10^3 or 4.92 x 10^2
2. The moon is 238,900 miles from the Earth. Estimate the distance as the product of a single digit number times a power of 10.
3. Write the number 0.0000000678 as the product of a single digit number times a power of 10.
4. Write the number 0.0000000000276 as the product of a single number times a power of 10.
5. Make a table of the powers of 10 from 10^5 to 10^-5.
1. To compare the two numbers, we need to convert them to the same power of 10.
2.75 x 10^3 can be written as 2750 x 10^2
Now we can compare:
2750 x 10^2 vs 4.92 x 10^2
Since 2750 is larger than 4.92, 2750 x 10^2 is larger than 4.92 x 10^2.
2. The distance from the Earth to the Moon can be estimated as the product of a single digit number (2) times a power of 10. Since the distance is 238,900 miles, we can estimate it as 2.389 x 10^5 miles.
3. 0.0000000678 can be written as 6.78 x 10^-8.
4. 0.0000000000276 can be written as 2.76 x 10^-11.
5. Here is a table of the powers of 10 from 10^5 to 10^-5:
| Power of 10 | Value |
|-------------|----------------------|
| 10^5 | 100,000 |
| 10^4 | 10,000 |
| 10^3 | 1,000 |
| 10^2 | 100 |
| 10^1 | 10 |
| 10^0 | 1 |
| 10^-1 | 0.1 |
| 10^-2 | 0.01 |
| 10^-3 | 0.001 |
| 10^-4 | 0.0001 |
| 10^-5 | 0.00001 |
1. Write 7,250,000 in scientific notation.
2. Write 0.0035621 in scientific notation.
3. Write 872,010,000,000 in scientific notation.
4. Write 0.00000000026 in scientific notation.
5. The distance between Earth and the planet Pluto is 3,241,600,000 miles. Write the distance in scientific notation.
1. To write 7,250,000 in scientific notation, we move the decimal point to the left until only one digit remains to the left of the decimal. In this case, we move the decimal point 6 places to the left, giving us 7250000. So, 7,250,000 in scientific notation is 7.25 x 10^6.
2. To write 0.0035621 in scientific notation, we move the decimal point to the right until a single non-zero digit remains to the left of the decimal. In this case, we move the decimal point 3 places to the right, giving us 35621. So, 0.0035621 in scientific notation is 3.5621 x 10^-3.
3. To write 872,010,000,000 in scientific notation, we move the decimal point to the left until only one digit remains to the left of the decimal. In this case, we move the decimal point 11 places to the left, giving us 8.72010000000. So, 872,010,000,000 in scientific notation is 8.7201 x 10^11.
4. To write 0.00000000026 in scientific notation, we move the decimal point to the right until a single non-zero digit remains to the left of the decimal. In this case, we move the decimal point 10 places to the right, giving us 26. So, 0.00000000026 in scientific notation is 2.6 x 10^-10.
5. To write 3,241,600,000 in scientific notation, we move the decimal point to the left until only one digit remains to the left of the decimal. In this case, we move the decimal point 9 places to the left, giving us 3241600000. So, 3,241,600,000 in scientific notation is 3.2416 x 10^9.
1. Order the following from least to greatest: 6.8 x 10^6 , 6 x 10^6 , 6.6 x 10^6 , 6.1 x 10^6
2. The diameter of the planet Mercury is 4.87 x 10^3 kilometers. The diameter of the planet Venus is 1.21 x 10^4 kilometers. The diameter of Earth is 1.28 x 10^4 kilometers. The diameter of Mars is 6.79 x 10^3 kilometers. Which planet has the smallest diameter?
3. Which of these numbers is the least?
a. 3.5 x 10^7
b. 3 x 10^7
c. 5 x 10^7
d. 5.5 x 10^7
4. Which is greater, 5.15 × 10^-4 or 6.35 × 10^-5
5. What do you notice between the negatives and the positive exponents?
1. To order the numbers, we compare the numerical values.
6 x 10^6 < 6.1 x 10^6 < 6.6 x 10^6 < 6.8 x 10^6
Therefore, the order from least to greatest is: 6 x 10^6, 6.1 x 10^6, 6.6 x 10^6, 6.8 x 10^6.
2. To compare the diameters of the planets, we compare the numerical values.
4.87 x 10^3 < 6.79 x 10^3 < 1.28 x 10^4 < 1.21 x 10^4
Therefore, the planet with the smallest diameter is Mercury.
3. To determine which number is the least, we compare the numerical values.
3 x 10^7 < 3.5 x 10^7 < 5 x 10^7 < 5.5 x 10^7
Therefore, the number 3 x 10^7 is the least.
4. To determine which number is greater, we compare the numerical values.
5.15 × 10^-4 > 6.35 × 10^-5
Therefore, 5.15 × 10^-4 is greater than 6.35 × 10^-5.
5. The relationship between the negative and positive exponents is that as the exponent decreases (moving from a positive to a negative exponent), the value of the number becomes smaller. For example, 10^3 is larger than 10^2, which is larger than 10^1. Conversely, as the exponent increases (moving from a negative to a positive exponent), the value of the number becomes larger. For example, 10^-3 is smaller than 10^-2, which is smaller than 10^-1.
Define: Metric System -
Define: Metric system as powers of 10 -
Define: Common US measures and conversions -
1. Convert the speed 1.000m/s (meters/second) to mi/h (miles/hour). Hint: 1m = 5280 ft and 1 inch = 2.54 cm
2. Use your weight in pounds to calculate kilograms and grams. Hint: 1kg = 2.205lb.
3. Write in standard format: 2.146e2
4. Write the number in e notation: 62360
5. Write in standard notation: 3.443 x 10^-7
Metric System: The metric system is a decimal-based measurement system that is used worldwide for scientific, industrial, and everyday purposes. It provides a standardized set of units for measuring length, mass, volume, time, temperature, and other quantities.
Metric system as powers of 10: The metric system is based on the concept of using powers of 10. The base unit is multiplied or divided by powers of 10 to create different units. For example, in the metric system, a kilometer is equal to 1000 meters, and a milliliter is one-thousandth of a liter.
Common US measures and conversions: In the United States, some commonly used measures include inches, feet, yards, miles, pounds, and ounces. Here are some common conversions:
- 1 inch = 2.54 centimeters
- 1 foot = 12 inches
- 1 yard = 3 feet
- 1 mile = 5280 feet
- 1 pound = 16 ounces
1. To convert the speed from meters/second to miles/hour, we need to perform a series of conversions.
1 meter = 5280/12 feet (since there are 5280 feet in a mile and 12 inches in a foot)
1 foot = 12 x 2.54 cm (since there are 12 inches in a foot and 2.54 centimeters in an inch)
1 mile = 5280 feet
1 meter/second = (5280/12) feet/second = (5280/12) x (12 x 2.54) cm/second = (5280/12) x 12 x 2.54/100 m/s
Next, we convert from meters/second to miles/hour:
1 mile = 5280 feet
1 hour = 60 minutes x 60 seconds
(1 meter/second) x [(5280/12) x 12 x 2.54/100] x (1 mile/5280 feet) x (60 minutes/1 hour) x (60 seconds/1 minute)
Simplifying this calculation gives us the speed in miles/hour.
2. To convert weight from pounds to kilograms and grams, we use the conversion factor:
1 kilogram = 2.205 pounds
To convert weight from pounds to kilograms, divide the weight in pounds by 2.205. To convert weight from pounds to grams, multiply the weight in pounds by 453.592.
3. 2.146e2 can be written in standard format as 214.6.
4. 62360 in e notation is 6.236 x 10^4.
5. 3.443 x 10^-7 in standard notation is 0.0000003443.