Miriam and Priya are dividing numbers written in scientific notation. (3 points)
Miriam’s expression: Priya’s expression:
2.8x109 2.8x102
1.4x104 1.4x10-3
Without completing the division, explain how can you determine that their answers will have the same value.
What is the value of their expressions written in scientific notation?
What is the value of their expressions written in standard form
thx bruh
a) You can determine this by looking at the power of 10 that is given. For example, when looking at 2.8 * 10^2, you know it would be 280 and that 1.4 * 10^-3 would be 0.0014. As for the 2.8x10^9 would be 2800000000 and that 1.4x10^4 would be 14000. You would need to move the the decimal place for the first one 0.0014 till you get 14. This means that you put 4 extra zeroes to 280, which is 280000. After that you can divide 28 by 14, without taking into account the zeroes, and you will get 2, which means your answer is 200000. For the second one, you also move decimal place 14000.0 to get 14, which means that you will need to take out 3 zeroes in 2800000000, you will get 2800000 and then without taking account the zeros, divide 28 by 14 and you will 2, which means your answer is also 200000.
b) 2 x 10^5 or 2E5
c) 2.8x109 = 2800000000 2.8x102 = 280
1.4x104 = 14000 1.4x10-3 = 0.0014
P.S I did not use a calculator for this one. So please check.
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hey there fellas
To determine if their answers will have the same value without completing the division, you can compare the exponents in both expressions.
In Miriam's expression, the exponent is 9, which means the number is multiplied by 10 raised to the power of 9.
In Priya's expression, the exponent is 2, which means the number is multiplied by 10 raised to the power of 2.
Since both expressions have a positive exponent, it means the numbers are greater than 1.
To compare the expressions, you can rewrite both of them so that their exponents are the same.
Miriam's expression: 2.8x109
Priya's expression: 2.8x102
To make the exponents the same, you can multiply Priya's expression by 107 (from 102 to 109). By doing this, the expressions become:
Miriam's expression: 2.8x109
Priya's expression: 280x109
Now, you can see that both expressions have the same base number (2.8) and the same exponent (109).
Therefore, their answers will have the same value.
Now, let's calculate the value of each expression written in scientific notation:
Miriam's expression: 2.8x109 = 2,800,000,000
Priya's expression: 280x109 = 280,000,000,000
And finally, let's convert their expressions to standard form:
Miriam's expression (standard form): 2.8 * 10^9 = 2,800,000,000
Priya's expression (standard form): 280 * 10^9 = 280,000,000,000