Express 473.5629 in base 10 as a binary number?
1 Answer
Explanation:
I wonder whether the number given should have been
First work on the integer part:
The first few powers of
#1, 2, 4, 8, 16, 32, 64, 128, 256, 512#
We find:
#473 = 256+128+64+16+8+1 = 111011001_2#
For the fractional part, we can repeatedly double and note down the integer part before discarding it to give the next binary digit:
#0.5629 * 2 = color(red)(1).1258#
#0.1258 * 2 = color(red)(0).2516#
#0.2516 * 2 = color(red)(0).5032#
#0.5032 * 2 = color(red)(1).0064#
#0.0064 * 2 = color(red)(0).0128#
#0.0128 * 2 = color(red)(0).0256#
#0.0256 * 2 = color(red)(0).0512#
#0.0512 * 2 = color(red)(0).1024#
#0.1024 * 2 = color(red)(0).2048#
#0.2048 * 2 = color(red)(0).4096#
#0.4096 * 2 = color(red)(0).8192#
#0.8192 * 2 = color(red)(1).6384#
#0.6384 * 2 = color(red)(1).2768#
#0.2768 * 2 = color(red)(0).5536#
#0.5536 * 2 = color(red)(1).1072#
#0.1072 * 2 = color(red)(0).2144#
#0.2144 * 2 = color(red)(0).4288#
#0.4288 * 2 = color(red)(0).8576#
#0.8576 * 2 = color(red)(1).7152#
#0.7152 * 2 = color(red)(1).4304#
#0.4304 * 2 = color(red)(0).8608#
#0.8608 * 2 = color(red)(1).7216#
#0.7216 * 2 = color(red)(1).4432#
#0.4432 * 2 = color(red)(0).8864#
#0.8864 * 2 = color(red)(1).7728#
#0.7728 * 2 = color(red)(1).5456#
#0.5456 * 2 = color(red)(1).0912#
#0.0912 * 2 = color(red)(0).1824#
#0.1824 * 2 = color(red)(0).3648#
#0.3648 * 2 = color(red)(0).7296#
#0.7296 * 2 = color(red)(1).4592#
#0.4592 * 2 = color(red)(0).9184#
#0.9184 * 2 = color(red)(1).8368#
#0.8368 * 2 = color(red)(1).6736#
...
Eventually the fractional part will repeat, and so will the binary expansion, but I will leave that to you to find.
For now, we can combine our integer and fractional parts to find:
#473.5625 = 111011001.1001_2#
#473.5629 ~~ 111011001.100100000001101000110110111001011_2#