Name: Use of Exponents to Express Small Numbers in Standard Form
Uploaded: 2019-07-19
Duration: 8 min 15 s
Description: In this video, we will learn how to express a number in its standard exponential form. Very large as well as very small numbers can be expressed in standard...

Question

An insect is on the $0$ point of a number line, hopping towards $1$ . She covers half the distance from her current location to $1$ with each hop. So, she will be at $1 / 2$ after one hop, $3 / 4$ after two hops, and so on.

Make a table showing the insect's location for the first $10$ hops.

Accepted Answer

Given that an insect is on the $0$ point of a number line, hopping towards $1$ . She covers half the distance from her current location to $1$ with each hop. So, she will be at $1 / 2$ after one hop, $3 / 4$ after two hops, and so on.

Distance covered in $1^{st}$ hop $= \frac{1}{2}$ and distance left $= 1 - \frac{1}{2} = \frac{1}{2}$

Distance covered in $2^{nd}$ hope $= \frac{1}{2} (\frac{1}{2}) + \frac{1}{2} = \frac{1}{4} + \frac{1}{2} = \frac{3}{4}$ and distance left $= 1 - \frac{3}{4} = \frac{1}{4}$ .

Similarly, we can find the insect's location in other hops as shown below-

No. of hops Distance covered Distance left

1 $\frac{1}{2}$ $1 - \frac{1}{2} = \frac{1}{2}$

2 $\frac{1}{2} (\frac{1}{2}) + \frac{1}{2} = \frac{3}{4}$ or $1 - \frac{1}{4}$ $1 - \frac{3}{4} = \frac{1}{4}$

3 $\frac{1}{2} (\frac{1}{4}) + \frac{3}{4} = \frac{1}{8} + \frac{3}{4} = \frac{7}{8}$ or $1 - \frac{1}{8}$ $1 - \frac{7}{8} = \frac{1}{8}$

4 $\frac{1}{2} (\frac{1}{8}) + \frac{7}{8} = \frac{1}{16} + \frac{7}{8} = \frac{15}{16}$ or $1 - \frac{1}{16}$ $1 - \frac{15}{16} = \frac{1}{16}$

5 $\frac{1}{2} (\frac{1}{16}) + \frac{15}{16} = \frac{1}{32} + \frac{15}{16} = \frac{31}{32}$ or $1 - \frac{1}{32}$ $1 - \frac{31}{32} = \frac{1}{32}$

6 $\frac{1}{2} (\frac{1}{32}) + \frac{31}{32} = \frac{1}{64} + \frac{31}{32} = \frac{63}{64}$ or $1 - \frac{1}{64}$ $1 - \frac{63}{64} = \frac{1}{64}$

7 $\frac{1}{2} (\frac{1}{64}) + \frac{63}{64} = \frac{1}{128} + \frac{63}{64} = \frac{127}{128}$ or $1 - \frac{1}{128}$ $1 - \frac{127}{128} = \frac{1}{128}$

8 $\frac{1}{2} (\frac{1}{128}) + \frac{127}{128} = \frac{1}{256} + \frac{127}{128} = \frac{255}{256}$ or $1 - \frac{1}{256}$ $1 - \frac{255}{256} = \frac{1}{256}$

9 $\frac{1}{2} (\frac{1}{256}) + \frac{255}{256} = \frac{1}{512} + \frac{255}{256} = \frac{511}{512}$ or $1 - \frac{1}{512}$ $1 - \frac{511}{512} = \frac{1}{512}$

10 $\frac{1}{2} (\frac{1}{512}) + \frac{511}{512} = \frac{1}{1024} + \frac{511}{512} = \frac{1023}{1024}$ or $1 - \frac{1}{1024}$ $1 - \frac{1023}{1024} = \frac{1}{1024}$

$X$	$1^{x}$	$2^{x}$	$3^{x}$	$4^{x}$	$5^{x}$	$6^{x}$	$7^{x}$	$8^{x}$	$9^{x}$	$10^{x}$
$1$	$1$	$2$
$2$	$1$	$4$
$3$	$1$	$8$
$4$	$1$	$16$
$5$	$1$	$32$
$6$	$1$	$64$
$7$	$1$	$128$
$8$	$1$	$256$
Ones digits of the powers	$1$	$2, 4, 8, 6$

$X$	$1^{x}$	$2^{x}$	$3^{x}$	$4^{x}$	$5^{x}$	$6^{x}$	$7^{x}$	$8^{x}$	$9^{x}$	$10^{x}$
$1$	$1$	$2$
$2$	$1$	$4$
$3$	$1$	$8$
$4$	$1$	$16$
$5$	$1$	$32$
$6$	$1$	$64$
$7$	$1$	$128$
$8$	$1$	$256$
Ones digits of the powers	$1$	$2, 4, 8, 6$

$X$	$1^{x}$	$2^{x}$	$3^{x}$	$4^{x}$	$5^{x}$	$6^{x}$	$7^{x}$	$8^{x}$	$9^{x}$	$10^{x}$
$1$	$1$	$2$
$2$	$1$	$4$
$3$	$1$	$8$
$4$	$1$	$16$
$5$	$1$	$32$
$6$	$1$	$64$
$7$	$1$	$128$
$8$	$1$	$256$
Ones digits of the powers	$1$	$2, 4, 8, 6$

$X$	$1^{x}$	$2^{x}$	$3^{x}$	$4^{x}$	$5^{x}$	$6^{x}$	$7^{x}$	$8^{x}$	$9^{x}$	$10^{x}$
$1$	$1$	$2$
$2$	$1$	$4$
$3$	$1$	$8$
$4$	$1$	$16$
$5$	$1$	$32$
$6$	$1$	$64$
$7$	$1$	$128$
$8$	$1$	$256$
Ones digits of the powers	$1$	$2, 4, 8, 6$

$X$	$1^{x}$	$2^{x}$	$3^{x}$	$4^{x}$	$5^{x}$	$6^{x}$	$7^{x}$	$8^{x}$	$9^{x}$	$10^{x}$
$1$	$1$	$2$
$2$	$1$	$4$
$3$	$1$	$8$
$4$	$1$	$16$
$5$	$1$	$32$
$6$	$1$	$64$
$7$	$1$	$128$
$8$	$1$	$256$
Ones digits of the powers	$1$	$2, 4, 8, 6$

An insect is on the $0$ point of a number line, hopping towards $1$ . She covers half the distance from her current location to $1$ with each hop. So, she will be at $1 / 2$ after one hop, $3 / 4$ after two hops, and so on.

Make a table showing the insect's location for the first $10$ hops.

Important Questions on Exponents and Powers

Learn and Prepare for any exam you want !

An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop. So, she will be at 1/2 after one hop, 3/4 after two hops, and so on. Make a table showing the insect's location for the first 10 hops.

Important Questions on Exponents and Powers

Learn and Prepare for any exam you want !

An insect is on the $0$ point of a number line, hopping towards $1$ . She covers half the distance from her current location to $1$ with each hop. So, she will be at $1 / 2$ after one hop, $3 / 4$ after two hops, and so on.

Make a table showing the insect's location for the first $10$ hops.