Thank you for visiting Work out the missing powers of 10 a tex 2 77 times 10 square 277000 tex b tex 7 4 div 10 square 0 00074. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
We need to find the exponent for the power of 10 that makes the equation in each part true. Let’s solve each one step by step.
--------------------------------------------
Part (a):
We have
[tex]$$2.77 \times 10^x = 277000.$$[/tex]
Isolate [tex]$10^x$[/tex] by dividing both sides by 2.77:
[tex]$$10^x = \frac{277000}{2.77}.$$[/tex]
Calculating the quotient gives:
[tex]$$\frac{277000}{2.77} = 100000.$$[/tex]
Since
[tex]$$10^5 = 100000,$$[/tex]
we have
[tex]$$x = 5.$$[/tex]
--------------------------------------------
Part (b):
The equation is
[tex]$$7.4 \div 10^x = 0.00074.$$[/tex]
Write this as:
[tex]$$\frac{7.4}{10^x} = 0.00074.$$[/tex]
Multiplying both sides by [tex]$10^x$[/tex], we obtain:
[tex]$$7.4 = 0.00074 \times 10^x.$$[/tex]
Now, solve for [tex]$10^x$[/tex]:
[tex]$$10^x = \frac{7.4}{0.00074}.$$[/tex]
Calculating the fraction:
[tex]$$\frac{7.4}{0.00074} = 10000.$$[/tex]
Since
[tex]$$10^4 = 10000,$$[/tex]
we deduce that
[tex]$$x = 4.$$[/tex]
--------------------------------------------
Part (c):
The equation is
[tex]$$9 \times 10^x = 9000000000.$$[/tex]
Divide both sides by 9 to isolate [tex]$10^x$[/tex]:
[tex]$$10^x = \frac{9000000000}{9}.$$[/tex]
This gives
[tex]$$10^x = 1000000000.$$[/tex]
Since
[tex]$$10^9 = 1000000000,$$[/tex]
we have
[tex]$$x = 9.$$[/tex]
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Part (d):
We start with
[tex]$$2.48 \div 10^x = 0.0000248.$$[/tex]
Rewrite it as:
[tex]$$\frac{2.48}{10^x} = 0.0000248.$$[/tex]
Multiply both sides by [tex]$10^x$[/tex]:
[tex]$$2.48 = 0.0000248 \times 10^x.$$[/tex]
Now, solve for [tex]$10^x$[/tex]:
[tex]$$10^x = \frac{2.48}{0.0000248}.$$[/tex]
Performing the calculation yields:
[tex]$$10^x = 100000.$$[/tex]
Since
[tex]$$10^5 = 100000,$$[/tex]
it follows that
[tex]$$x = 5.$$[/tex]
--------------------------------------------
Part (e):
The equation is
[tex]$$9.1 \times 10^x = 910.$$[/tex]
Divide both sides by 9.1:
[tex]$$10^x = \frac{910}{9.1}.$$[/tex]
This simplifies to:
[tex]$$10^x = 100.$$[/tex]
Since
[tex]$$10^2 = 100,$$[/tex]
we deduce that
[tex]$$x = 2.$$[/tex]
--------------------------------------------
Part (f):
We have the equation
[tex]$$39.4 \div 10^x = 0.0394.$$[/tex]
Express it as:
[tex]$$\frac{39.4}{10^x} = 0.0394.$$[/tex]
Multiply both sides by [tex]$10^x$[/tex]:
[tex]$$39.4 = 0.0394 \times 10^x.$$[/tex]
Now, solve for [tex]$10^x$[/tex]:
[tex]$$10^x = \frac{39.4}{0.0394}.$$[/tex]
This gives:
[tex]$$10^x = 1000.$$[/tex]
And since
[tex]$$10^3 = 1000,$$[/tex]
we find
[tex]$$x = 3.$$[/tex]
--------------------------------------------
Final Answers:
a) [tex]$x = 5$[/tex]
b) [tex]$x = 4$[/tex]
c) [tex]$x = 9$[/tex]
d) [tex]$x = 5$[/tex]
e) [tex]$x = 2$[/tex]
f) [tex]$x = 3$[/tex]
--------------------------------------------
Part (a):
We have
[tex]$$2.77 \times 10^x = 277000.$$[/tex]
Isolate [tex]$10^x$[/tex] by dividing both sides by 2.77:
[tex]$$10^x = \frac{277000}{2.77}.$$[/tex]
Calculating the quotient gives:
[tex]$$\frac{277000}{2.77} = 100000.$$[/tex]
Since
[tex]$$10^5 = 100000,$$[/tex]
we have
[tex]$$x = 5.$$[/tex]
--------------------------------------------
Part (b):
The equation is
[tex]$$7.4 \div 10^x = 0.00074.$$[/tex]
Write this as:
[tex]$$\frac{7.4}{10^x} = 0.00074.$$[/tex]
Multiplying both sides by [tex]$10^x$[/tex], we obtain:
[tex]$$7.4 = 0.00074 \times 10^x.$$[/tex]
Now, solve for [tex]$10^x$[/tex]:
[tex]$$10^x = \frac{7.4}{0.00074}.$$[/tex]
Calculating the fraction:
[tex]$$\frac{7.4}{0.00074} = 10000.$$[/tex]
Since
[tex]$$10^4 = 10000,$$[/tex]
we deduce that
[tex]$$x = 4.$$[/tex]
--------------------------------------------
Part (c):
The equation is
[tex]$$9 \times 10^x = 9000000000.$$[/tex]
Divide both sides by 9 to isolate [tex]$10^x$[/tex]:
[tex]$$10^x = \frac{9000000000}{9}.$$[/tex]
This gives
[tex]$$10^x = 1000000000.$$[/tex]
Since
[tex]$$10^9 = 1000000000,$$[/tex]
we have
[tex]$$x = 9.$$[/tex]
--------------------------------------------
Part (d):
We start with
[tex]$$2.48 \div 10^x = 0.0000248.$$[/tex]
Rewrite it as:
[tex]$$\frac{2.48}{10^x} = 0.0000248.$$[/tex]
Multiply both sides by [tex]$10^x$[/tex]:
[tex]$$2.48 = 0.0000248 \times 10^x.$$[/tex]
Now, solve for [tex]$10^x$[/tex]:
[tex]$$10^x = \frac{2.48}{0.0000248}.$$[/tex]
Performing the calculation yields:
[tex]$$10^x = 100000.$$[/tex]
Since
[tex]$$10^5 = 100000,$$[/tex]
it follows that
[tex]$$x = 5.$$[/tex]
--------------------------------------------
Part (e):
The equation is
[tex]$$9.1 \times 10^x = 910.$$[/tex]
Divide both sides by 9.1:
[tex]$$10^x = \frac{910}{9.1}.$$[/tex]
This simplifies to:
[tex]$$10^x = 100.$$[/tex]
Since
[tex]$$10^2 = 100,$$[/tex]
we deduce that
[tex]$$x = 2.$$[/tex]
--------------------------------------------
Part (f):
We have the equation
[tex]$$39.4 \div 10^x = 0.0394.$$[/tex]
Express it as:
[tex]$$\frac{39.4}{10^x} = 0.0394.$$[/tex]
Multiply both sides by [tex]$10^x$[/tex]:
[tex]$$39.4 = 0.0394 \times 10^x.$$[/tex]
Now, solve for [tex]$10^x$[/tex]:
[tex]$$10^x = \frac{39.4}{0.0394}.$$[/tex]
This gives:
[tex]$$10^x = 1000.$$[/tex]
And since
[tex]$$10^3 = 1000,$$[/tex]
we find
[tex]$$x = 3.$$[/tex]
--------------------------------------------
Final Answers:
a) [tex]$x = 5$[/tex]
b) [tex]$x = 4$[/tex]
c) [tex]$x = 9$[/tex]
d) [tex]$x = 5$[/tex]
e) [tex]$x = 2$[/tex]
f) [tex]$x = 3$[/tex]
Thank you for reading the article Work out the missing powers of 10 a tex 2 77 times 10 square 277000 tex b tex 7 4 div 10 square 0 00074. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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