Exercise 20 Page 72

We want to determine which of the given equations are true. To do so, we will simplify the expression on the left-hand side of each equation. Next, we will write both sides of each equation in standard form to compare the obtained numbers.

First Equation

Let's check whether the first equation is true. (4.7 * 10^4)+ (8* 10^4 ) ? = 1.27 * 10^5 We can do the addition to simplify the left-hand side of the equation. Note that both terms on the left-hand side already have the same power of 10. Finally, we will write both sides of the equation in standard form.

Since we obtained a true statement, the equation is true.

Second Equation

Now we will check whether the second equation is true. (7.08 * 10^3 )+(2.21* 10^3 ) ? = 9.29 * 10^6 Let's do the addition to simplify the left-hand side of the equation. Note that both terms on the left-hand side already have the same power of 10.

(7.08 * 10^3 )+ (2.21* 10^3 ) ? = 9.29 * 10^6

RemovePar

Remove parentheses

7.08 * 10^3+2.21* 10^3 ? = 9.29 * 10^6

FactorOut

Factor out 10^3

(7.08+2.21 ) * 10^3 ? = 9.29 * 10^6

AddTerms

Add terms

9.29 * 10^3 ? = 9.29 * 10^6

Finally, we will write both sides of the equation in standard form.

9.29 * 10^3 ? = 9.29 * 10^6

CalcPow

Calculate power

9.29 * 1000 ? = 9.29 * 1 000 000

Multiply

Multiply

9290 ≠ 9 290 000 *

Since we obtained a false statement, the equation is not true.

Third Equation

Let's check whether the third equation is true. (5.43 * 10^8 )- (2.33* 10^8 ) ? = 3.1 * 10^4 We can do the subtraction to simplify the left-hand side of the equation. Note that both terms on the left-hand side already have the same power of 10.

(5.43 * 10^8 )- (2.33* 10^8 ) ? = 3.1 * 10^4

RemovePar

Remove parentheses

5.43 * 10^8-2.33* 10^8 ? = 3.1 * 10^4

FactorOut

Factor out 10^8

(5.43-2.33 ) * 10^8 ? = 3.1 * 10^4

SubTerm

Subtract term

3.1 * 10^8 ? = 3.1 * 10^4

Finally, we will write both sides of the equation in standard form.

3.1 * 10^8 ? = 3.1 * 10^4

CalcPow

Calculate power

3.1 * 100 000 000 ? = 3.1 * 10 000

Multiply

Multiply

310 000 000 ≠ 31 000 *

Since we obtained a false statement, the equation is not true.

Fourth Equation

Now we will check whether the fourth equation is true. (9.35 * 10^6 )- (6.7* 10^6 ) ? = 2.65 * 10^6 Let's do the subtraction to simplify the left-hand side of the equation. Note that both terms on the left-hand side already have the same power of 10.

(9.35 * 10^6 )- (6.7* 10^6 ) ? = 2.65 * 10^6

RemovePar

Remove parentheses

9.35 * 10^6-6.7* 10^6 ? = 2.65 * 10^6

FactorOut

Factor out 10^6

(9.35-6.7 ) * 10^6 ? = 2.65 * 10^6

SubTerm

Subtract term

2.65 * 10^6 ? = 2.65 * 10^6

Finally, we will write both sides of the equation in standard form.

2.65 * 10^6 ? = 2.65 * 10^6

CalcPow

Calculate power

2.65 * 1 000 000 ? = 2.65 * 1 000 000

Multiply

Multiply

2 650 000 = 2 650 000 ✓

Since we obtained a true statement, the equation is true.

Conclusion

We found that the first and fourth equations are true.