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Transcript. Explore the concept of multiplying by powers of 10. Learn about the pattern of adding zeros when multiplying by 10 and the use of exponents as a shorthand for repeated multiplication. Discover the connection between the number of times 10 is multiplied and the number of zeros in the product. Created by Sal Khan.
- 6 min
- Sal Khan
Transcript. Exponents are a way of simplifying the notation for repeated multiplication. When using a base of 10, the exponent tells you how many times to multiply 10 by itself. Converting between exponential notation and standard notation is straightforward: for example, 10 to the second power is the same as 10 times 10, or 100.
- 4 min
- You are right about ten, but 2^2=20 isn't correct.
- Thank you 🙏🙏
- 10 to -1 power is equal to 1/10 when you have a negative exponent you always make it a fraction. For example 5 to the -1 power is equal to 1/5. Hop...
- That is correct. But you have to make sure you are adding the zeroes to the first digit, one, or else your number may be 10 times too high.
- It would be 1 followed by 1,000,000 zeroes. Yeah. That's a lot. I think it's called a Googol, and it's written as 10^1000000.
- Positive Powers of 10
- Negative Powers of 10
- 2 to The Power of 10
- Calculating Powers of 10
The powers of 10 have some specific names (though not all powers) for some specific powers. For example, 106(10 to the power of 6) is known as a 'million' and the SI prefix of 10 power 6 is 'giga' which is represented by the SI symbol G. Similarly, we have some specific names for some positive powers of 10 which are given in the following table.
The negative powers of 10 are expressed in a different way. We know that a negative power (negative exponent) is defined as the multiplicative inverse of the base. This means that we write the reciprocal of the number and then solve it like positive exponents. For example, (4/5)-2 can be written as (5/4)2. Similarly, a negative power of 10, like 10...
It should be noted that 2 to the power of 10 is not the same as 10 to the power of 2. 2 to the power of 10 means a number in which 2 is the base and 10 is the exponent. This is written as 210and this means 2 is multiplied ten times, that is, 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024.
In order to calculate the sum, difference, product, and quotient of powers of 10, we can first find the values of powers of 10 and then do the respective operation. For example, 103/102= 1000/100 = 10. But sometimes, this procedure is difficult if the exponent is very large. In such cases, the following procedures would help.
To evaluate a power of 10 , we multiply the base ( 10) by itself the exponent amount of times. Example: 10 5 has an exponent of 5 , so we multiply 10 times itself 5 times: 10 5 = 10 × 10 × 10 × 10 × 10 = 100,000.
Power of 10. Visualisation of powers of 10 from one to 1 billion. A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few non-negative powers of ten are:
Dividing! So we divide by 10 each time, which is the same as multiplying by 1 10. Example: What is 5 × 10 -3 ? 5 × 10 -3 = 5 × 1 10 × 1 10 × 1 10. = 0.005. But it is easier to use this handy rule: For negative powers of 10, move the decimal point to the left. So Negatives just go the other way.
2 Count the number of \bf {10} 10s in the expression to create the power of \bf {10} 10. 45,000=45 \times 10 \times 10 \times 10 45,000 = 45 × 10 × 10 × 10. There are 3 3 tens being multiplied. Use 10 10 as the base and 3 3 as the exponent. 3 Write the equation.
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